Complete and complete moment convergence for randomly weighted sums of \(\rho^*\)-mixing random variables and its applications. (English) Zbl 1439.60034
The authors provide several sufficient conditions for the complete and complete moment convergence of double-indexed randomly weighted sums of \(\rho^*\)-mixing random variables. As applications, they study the convergence of the state observers of linear-time-invariant systems and the complete consistency for the weighted estimator in nonparametric regression models based on \(\rho^*\)-mixing random errors; and perform relevant numerical simulations.
Reviewer: George Stoica (Saint John)
MSC:
| 60F15 | Strong limit theorems |
| 60G20 | Generalized stochastic processes |
| 93E24 | Least squares and related methods for stochastic control systems |
Keywords:
\(\rho^*\)-mixing random variables; randomly weighted sums; complete moment convergence; complete convergence; linear-time-invariant system; nonparametric regression modelReferences:
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